Given a vector space V, its projectivization P(V), sometimes written P(V-0), is the set of equivalence classes x∼lambdax for any lambda!=0 in V-0. For example, complex projective space has homogeneous coordinates [x_0,...,x_n], with not all x_i=0.

The projectivization is a manifold with one less dimension than V. In fact, it is covered by the n+1 affine coordinate charts,


See also

Complex Projective Space, Manifold, Vector Space

This entry contributed by Todd Rowland

Explore with Wolfram|Alpha

Cite this as:

Rowland, Todd. "Projectivization." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

Subject classifications